Valeria Mele

Deconvolution of 3d fluorescence microscopy images using graphics processing units

We consider the deconvolution of 3D Fluorescence Microscopy RGB images, describing the benefits arising from facing medical imaging problems on modern graphics processing units (GPUs), that are non expensive parallel processing devices available on many up-to-date personal computers. We found that execution time of CUDA version is about 2 orders of magnitude less than the one of sequential algorithm. Anyway, the experiments lead some reflections upon the best setting for the CUDA-based algorithm. That is, we notice the need to model the GPUs architectures and their characteristics to better describe the performance of GPU-algorithms and what we can expect of them.

A Double Adaptive Algorithm for Multidimensional Integration on Multicore Based HPC Systems

In this work, a parallel double adaptive algorithm for the computation of a multidimensional integral on multicore based multicomputer systems is described. This new algorithm is the revision of a procedure developed by one of the present authors for multicomputer systems, with the aim to introduce features for an efficient implementation in multicore based hierarchical environments. Two different adaptive strategies have been combined together in the algorithm: a first procedure is responsible for load balancing among the system nodes and a second one is responsible for coordinating the cores within a single node. The performance is analyzed and experimental results on a Blade Server with 8 nodes and 2 quad-core CPUs per node have been achieved.

A study on adaptive algorithms for numerical quadrature on heterogeneous GPU and multicore based systems

In this work, a parallel adaptive algorithm for the computation of a multidimensional integral on heterogeneous GPU and multicore based systems is described. Two different strategies have been combined together in the algorithm: a first procedure is responsible for the load balancing among the threads on the multicore CPU and a second one is responsible for an efficient execution on the GPU of the computational kernel. The performance is analyzed and experimental results on a system with a quad-core CPUs and two GPUs have been achieved.

ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

A software package for numerical inversion of Laplace transforms computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function. The software provides a controlled accuracy, i.e. it dynamically computes the so-called maximum attainable accuracy such that numerical results are provided within the greatest value between the user’s required accuracy and the maximum attainable accuracy. This is done because the intrinsic ill posedness of the real inversion problem sometime may prevent to reach the desired accuracy. The method implemented is based on a Laguerre polynomial series expansion of the inverse function and belongs to the class of polynomial-type methods of inversion of the Laplace transform, formally characterized as Collocation methods (C-methods).

Toward a fully parallel multigrid in time algorithm in PETSc environment: A case study in ocean models

We consider linear systems that arise from the discretization of evolutionary models. Typically, solution algorithms are based on a time-stepping approach, solving for one time step after the other. Parallelism is limited to the spatial dimension only. Because time is sequential in nature, the idea of simultaneously solving along time steps is not intuitive. One approach to achieve parallelism in time direction is MGRIT algorithm [7], based on multigrid reduction (MGR) techniques. Here we refer to this approach as MGR-1D. Other kind of approach is the space-time multigrid, where time is simply another dimension in the grid. Analougsly, we refer to this approach as MGR-4D. In this work, motivated by the need of maximizing the availability of new algorithms to climate science, we propose a new parallel approach that mixes both the MGR-1D idea and classical space multigrid methods. We refer to it as the MGR3D+1 approach. Moreover, we discuss their implementation in the high performance scientific library PETSc, as starting point to develope more efficient and scalable algorithms in ocean models.

A Loosely Coordinated Model for Heap-Based Priority Queues in Multicore Environments

Heap-based priority queues are very common dynamical data structures used in several fields, ranging from operating systems to scientific applications. However, the rise of new multicore CPUs introduced new challenges in the process of design of these data structures: in addition to traditional requirements like correctness and progress, the scalability is of paramount importance. It is a common opinion that these two demands are partially in conflict each other, so that in these computational environments it is necessary to relax the requirements of correctness and linearizability to achieve high performances. In this paper we introduce a loosely coordinated approach for the management of heap based priority queues on multicore CPUs, with the aim to realize a tradeoff between efficiency and sequential correctness. The approach is based on a sharing of information among only a small number of cores, so that to improve performance without completely losing the features of the data structure. The results obtained on a scientific problem show significant benefits both in terms of parallel efficiency, as well as in term of numerical accuracy.

Algorithm 946: ReLIADiff—A C++ Software Package for Real Laplace Transform Inversion based on Algorithmic Differentiation

Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is used for calculating function values of the inverse Laplace transform. The software requires transform values at arbitrary points in the complex plane. We developed a software package, called ReLIADiff, which is a modification of Algorithm 662 using transform values at arbitrary points on real axis. ReLIADiff, implemented in C++, relies on TADIFF software package designed for Algorithmic Differentiation. In this article, we present ReLIADiff focusing on its design principles, performance, and use.

Mathematical approach to the performance evaluation of three dimensional variational data assimilation

We analyse and discuss the performance of a decomposition approach introduced for solving large scale Variational Data Assimilation (DD-VAR DA) problems. Our performance analysis uses a set of matrices (decomposition and execution)[9], built to highlight the dependency relationship among component parts of a computational problem and/or among operators of the algorithm that solves the problem [10?], that are the fundamental characteristics of an algorithm. We will show how performance metrics depend on the complexity of the algorithm and on parameters characterizing the structure of the two matrices, like their number of rows and columns. We use a new definition of speed up, involving the scale-up factor which measure the performance gain in terms of time complexity reduction, to describe the non-linear behavior of the performance gain.

Mathematical Approach to the Performance Evaluation of Matrix Multiply Algorithm

Matrix multiplication (MM) is a computationally-intensive operation in many algorithms used in scientific computations. Not only one of the kernels in numerical linear algebra, the problem of matrix multiplication is also fundamental for almost all matrix problems such as least square and eigenvalues problem. The performance analysis of the MM needs to be re-evaluated to find out the best-practice algorithm on novel architectures. This motivated the analysis which is presented in this article and which is carried out by means of the new modelling framework that the authors have already introduced (L. D’Amore et al. On a Mathematical Approach for Analyzing Parallel Algorithms, 2015). The model exploits the knowledge of the algorithm and the multilevel parallelism of the target architecture and it could help the researchers for designing optimized MM implementations.

Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case

We are concerned with Gaver’s formula, which is at the heart of a numerical algorithm, widely used in scientific and engineering applications, for computing approximations of inverse Laplace transform in multi-precision arithmetic systems. We demonstrate that, once parameters n (i.e. the number of terms of Gaver’s formula) and (i.e. an upper bound on noise on data) are given, then the number of correct significant digits of computed values of the inverse function is bounded above by . In case of noise free data this number is arbitrarily large, as it is bounded below by n. We establish the requirement of the multi-precision system ensuring that the quality of numerical results is fulfilled. Experiments and comparisons validate the effectiveness of such approach.